Asymptotic and Finite Frame Length Analysis of Frame Asynchronous Coded Slotted ALOHA

We consider a frame-asynchronous coded slotted ALOHA (FA-CSA) system where users become active according to a Poisson random process. In contrast to standard frame-synchronous CSA (FS-CSA), users transmit a first replica of their message in the slot following their activation and other replicas uniformly at random in a number of subsequent slots. We derive the (approximate) density evolution that characterizes the asymptotic performance of FA-CSA when the frame length goes to infinity. We show that, if users can monitor the system before they start transmitting, a boundary-effect similar to that of spatially-coupled codes occurs, which greatly improves the decoding threshold as compared to FS-CSA. We also derive analytical approximations of the error floor (EF) in the finite frame length regime. We show that FA-CSA yields in general lower EF, better performance in the waterfall region, and lower average delay, as compared to FS-CSA.Comment: 5 pages, 6 figures. Updated notation, terminology, and typo

On Frame Asynchronous Coded Slotted ALOHA: Asymptotic, Finite Length, and Delay Analysis

We consider a frame asynchronous coded slotted ALOHA (FA-CSA) system for uncoordinated multiple access, where users join the system on a slot-by-slot basis according to a Poisson random process and, in contrast to standard frame synchronous CSA (FS-CSA), users are not frame-synchronized. We analyze the performance of FA-CSA in terms of packet loss rate and delay. In particular, we derive the (approximate) density evolution that characterizes the asymptotic performance of FA-CSA when the frame length goes to infinity. We show that, if the receiver can monitor the system before anyone starts transmitting, a boundary effect similar to that of spatially-coupled codes occurs, which greatly improves the iterative decoding threshold. Furthermore, we derive tight approximations of the error floor (EF) for the finite frame length regime, based on the probability of occurrence of the most frequent stopping sets. We show that, in general, FA-CSA provides better performance in both the EF and waterfall regions as compared to FS-CSA. Moreover, FA-CSA exhibits better delay properties than FS-CSA.Comment: 13 pages, 12 figures. arXiv admin note: substantial text overlap with arXiv:1604.0629

Towards a System Theoretic Approach to Wireless Network Capacity in Finite Time and Space

In asymptotic regimes, both in time and space (network size), the derivation of network capacity results is grossly simplified by brushing aside queueing behavior in non-Jackson networks. This simplifying double-limit model, however, lends itself to conservative numerical results in finite regimes. To properly account for queueing behavior beyond a simple calculus based on average rates, we advocate a system theoretic methodology for the capacity problem in finite time and space regimes. This methodology also accounts for spatial correlations arising in networks with CSMA/CA scheduling and it delivers rigorous closed-form capacity results in terms of probability distributions. Unlike numerous existing asymptotic results, subject to anecdotal practical concerns, our transient one can be used in practical settings: for example, to compute the time scales at which multi-hop routing is more advantageous than single-hop routing

Stable Throughput and Delay Analysis of a Random Access Network With Queue-Aware Transmission

In this work we consider a two-user and a three-user slotted ALOHA network with multi-packet reception (MPR) capabilities. The nodes can adapt their transmission probabilities and their transmission parameters based on the status of the other nodes. Each user has external bursty arrivals that are stored in their infinite capacity queues. For the two- and the three-user cases we obtain the stability region of the system. For the two-user case we provide the conditions where the stability region is a convex set. We perform a detailed mathematical analysis in order to study the queueing delay by formulating two boundary value problems (a Dirichlet and a Riemann-Hilbert boundary value problem), the solution of which provides the generating function of the joint stationary probability distribution of the queue size at user nodes. Furthermore, for the two-user symmetric case with MPR we obtain a lower and an upper bound for the average delay without explicitly computing the generating function for the stationary joint queue length distribution. The bounds as it is seen in the numerical results appear to be tight. Explicit expressions for the average delay are obtained for the symmetrical model with capture effect which is a subclass of MPR models. We also provide the optimal transmission probability in closed form expression that minimizes the average delay in the symmetric capture case. Finally, we evaluate numerically the presented theoretical results.Comment: Submitted for journal publicatio

Interference suppression and diversity for CDMA systems

In code-division multiple-access (CDMA) systems, due to non-orthogonality of the spreading codes and multipath channels, the desired signal suffers interference from other users. Signal fading due to multipath propagation is another source of impairment in wireless CDMA systems, often severely impacting performance. In this dissertation, reduced-rank minimum mean square error (MMSE) receiver and reduced-rank minimum variance receiver are investigated to suppress interference; transmit diversity is applied to multicarrier CDMA (MC-CDMA) systems to combat fading; packet combing is studied to provide both interference suppression and diversity for CDMA random access systems. The reduced-rank MMSE receiver that uses a reduced-rank estimated covariance matrix is studied to improve the performance of MMSE receiver in CDMA systems. It is shown that the reduced-rank MMSE receiver has much better performance than the full-rank MMSE receiver when the covariance matrix is estimated by using a finite number of data samples and the desired signal is in a low dimensional subspace. It is also demonstrated that the reduced-rank minimum variance receiver outperforms the full-rank minimum variance receiver. The probability density function of the output SNR of the full-rank and reduced-rank linear MMSE estimators is derived for a general linear signal model under the assumption that the signals and noise are Gaussian distributed. Space-time coding that is originally proposed for narrow band systems is applied to an MC-CDMA system in order to get transmit diversity for such a wideband system. Some techniques to jointly decode the space-time code and suppress interference are developed. The channel estimation using either pilot channels or pilot symbols is studied for MC-CDMA systems with space-time coding. Performance of CDMA random access systems with packet combining in fading channels is analyzed. By combining the current retransmitted packet with all its previous transmitted copies, the receiver obtains a diversity gain plus an increased interference and noise suppression gain. Therefore, the bit error rate dramatically decreases with the number of transmissions increasing, which in turn improves the system throughput and reduces the average delay

Channel-Aware Random Access in the Presence of Channel Estimation Errors

In this work, we consider the random access of nodes adapting their transmission probability based on the local channel state information (CSI) in a decentralized manner, which is called CARA. The CSI is not directly available to each node but estimated with some errors in our scenario. Thus, the impact of imperfect CSI on the performance of CARA is our main concern. Specifically, an exact stability analysis is carried out when a pair of bursty sources are competing for a common receiver and, thereby, have interdependent services. The analysis also takes into account the compound effects of the multipacket reception (MPR) capability at the receiver. The contributions in this paper are twofold: first, we obtain the exact stability region of CARA in the presence of channel estimation errors; such an assessment is necessary as the errors in channel estimation are inevitable in the practical situation. Secondly, we compare the performance of CARA to that achieved by the class of stationary scheduling policies that make decisions in a centralized manner based on the CSI feedback. It is shown that the stability region of CARA is not necessarily a subset of that of centralized schedulers as the MPR capability improves.Comment: The material in this paper was presented in part at the IEEE International Symposium on Information Theory, Cambridge, MA, USA, July 201

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